Multi-GPU Implementation of the Minimum Volume Simplex Analysis Algorithm for Hyperspectral Unmixing

Spectral unmixing is an important task in remotely sensed hyperspectral data exploitation. The linear mixture model has been widely used to unmix hyperspectral images by identifying a set of pure spectral signatures, called endmembers, and estimating their respective abundances in each pixel of the scene. Several algorithms have been proposed in the recent literature to automatically identify endmembers, even if the original hyperspectral scene does not contain any pure signatures. A popular strategy for endmember identification in highly mixed hyperspectral scenes has been the minimum volume simplex analysis (MVSA), known to be a computationally very expensive algorithm. This algorithm calculates the minimum volume enclosing simplex, as opposed to other algorithms that perform maximum simplex volume analysis (MSVA). The high computational complexity of MVSA, together with its very high memory requirements, has limited its adoption in the hyperspectral imaging community. In this paper, we develop several optimizations to the MVSA algorithm. The main computational task of MVSA is the solution of a quadratic optimization problem with equality and inequality constraints, with the inequality constraints being in the order of the number of pixels multiplied by the number of endmembers. As a result, storing and computing the inequality constraint matrix is highly inefficient. The first optimization presented in this paper uses algebra operations in order to reduce the memory requirements of the algorithm. In the second optimization, we use graphics processing units (GPUs) to effectively solve (in parallel) the quadratic optimization problem involved in the computation of MVSA. In the third optimization, we extend the single GPU implementation to a multi-GPU one, developing a hybrid strategy that distributes the computation while taking advantage of GPU accelerators at each node. The presented optimizations are tested in different analysis scenarios (using both synthetic - nd real hyperspectral data) and shown to provide state-of-the-art results from the viewpoint of unmixing accuracy and computational performance. The speedup achieved using the full GPU cluster compared to the CPU implementation in tenfold in a real hyperspectral image.